Of late there has been a surge of interest in localized phonon polariton resonators which allow for the subdiffraction confinement of light in the midinfrared spectral region by coupling to optical phonons at the surface of polar dielectrics. Resonators are generally etched on deep substrates which support propagative surface phonon polariton resonances. Recent experimental work has shown that understanding the coupling between localized and propagative surface phonon polaritons in these systems is vital to correctly describing the system resonances. In this paper we comprehensively investigate resonators composed of arrays of cylindrical SiC resonators on SiC substrates. Our bottom-up approach, starting from the resonances of single, free-standing cylinders and isolated substrates, and exploiting both numerical and analytical techniques, allows us to develop a consistent understanding of the parameter space of those resonators, putting on firmer ground this blossoming technology.